Question

the sum of the digits of a two digitnumber is 12 .If the digits are reversed the new number is 12 less than twice the original number.Find the numer

Answer 1

Let the tens digit of the Number be x and units digit be y,
then number is 10x + y

Given:  x + y = 12  ......................(1)

When digits are reversed

=> 10y + x = 2(10x + y) - 12
=> 19x - 8y = 12 .......................(2)

Solving (1) and (2), we get x=4 and y=8

So the Number is 48

Answer 2

Let a two digit number = x + 10y
A/C to question,
sum of digits of number = 12
⇒ x + y = 12 ------(1)

Now, digits are reversed then new number = y + 10x
A/c to question,
New number = 2(original number ) - 12
⇒y + 10x = 2(x + 10y) - 12
⇒ y + 10x = 2x + 20y - 12
⇒ 8x - 19y = -12
⇒ -8x + 19y = 12 -------(2)

Solve equations (1) and (2),
8y + 19y = 12 × 8 + 12 = 108
27y =108⇒ y = 4 , put it in equation (1),
x = 8

Hence, original number = x + 10y
= 8 + 10 × 4 = 8 + 40 = 48